The classical almost sure convergence of the normed supercritical Galton-Watson branching process with finite mean is obtained by a new method which does not involve probability generating functions.
D. R. Grey. "A New Look at Convergence of Branching Processes." Ann. Probab. 8 (2) 377 - 380, April, 1980. https://doi.org/10.1214/aop/1176994785